Judges for the 10th U.S. Circuit Court of Appeals on Tuesday rejected a challenge to Nathan Dunlap’s armed-robbery conviction, which was used to secure the death penalty against the Chuck E. Cheese killer.

The decision is a blow to Dunlap’s legal team, which had hoped to upend the robbery conviction as a way of unsettling Dunlap’s ultimate sentence.

Dunlap was sentenced in 1996 to die for killing four people at an Aurora Chuck E. Cheese restaurant. After his arrest in the killings — but before the trial — Dunlap was charged and tried for robbing a Burger King. Prosecutors used the robbery conviction as a building block for the death penalty.

Dunlap’s attorneys argue the robbery trial should have been moved from Arapahoe County because of pretrial publicity about the Chuck E. Cheese murders.

But a three-judge panel at the 10th Circuit rejected that argument, saying the case wasn’t an extreme example of pretrial publicity.

“Having reviewed the media coverage, we agree . . . that the state court’s decision was not an unreasonable application of clearly established federal law,” the judges wrote.

The judges also rejected an argument that prosecutors had unfairly prejudiced jurors during closing arguments.

Dunlap’s 10th Circuit appeal of his robbery conviction is a prelude to the much bigger appeal of his death sentence, which is expected to be heard by the appeals court next year. In that appeal, Dunlap has argued that his attorney in the death-penalty trial erred by not raising mitigating evidence that Dunlap suffers from mental illness.

Dunlap is the longest-serving inmate on Colorado’s death row. No execution date has been set.

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